Ok, yes and no.... mechanically and spec wise then yes they are the same... there are of course subtle differences which make no difference to the performance but are a result of Audi using up the parts bin for the change over to facelift S3's...
One example of this is the bevel box bracket... an AMK S3 (Dane's) that is in for rods has a cast alloy bracket supporting the bevel box to the engine block whereas mine (also an AMK) has a pressed steel one... there will also be revisions to parts that change slightly over the years such as later version coil packs and stuff... depends where you want to go with it all...
At the end of the day, AMK and BAM map up the same... there is no compelling reason to choose BAM over AMK and vice versa other than BAM are in newer S3's... if you can afford to buy a newer S3 you will get a BAM, go for a changeover facelift and you get an AMK...
Same internals, same head... the earlier AMK's had the drillings for the SAI blocked with steel ball bearings as heads were being used up but are still the same small port head the BAM have (and the APY for that matter).
The differences are minimal and largely academic
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